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ANNEXU.K.
Appendix B Flight performance calculations
B2ENGINE THRUSTU.K.
The propulsive force produced by each engine is one of five quantities that need to be defined at the ends of each flight path segment (the others being height, speed, power setting and bank angle). Net thrust represents the component of engine gross thrust that is available for propulsion. For aerodynamic and acoustical calculations, the net thrust is referred to standard air pressure at mean sea level. This is known as corrected net thrust, Fn/δ.
This will be either the net thrust available when operating at a specified thrust rating, or the net thrust that results when the thrust-setting parameter is set to a particular value. For a turbojet or turbofan engine operating at a specific thrust rating, corrected net thrust is given by the equation
| Fn/δ = E + F · Vc + GA· h + GB· h2 + H · T | (B-1) |
where
is the net thrust per engine, lbf
is the ratio of the ambient air pressure at the aeroplane to the standard air pressure at mean sea level, i.e., to 101,325 kPa (or 1 013,25 mb) [ref. 1]
is the corrected net thrust per engine, lbf
is the calibrated airspeed, kt
is the ambient air temperature in which the aeroplane is operating, °C, and
are engine thrust constants or coefficients for temperatures below the engine flat rating temperature at the thrust rating in use (on the current segment of the takeoff/climbout or approach flight path), lb.s/ft, lb/ft, lb/ft2, lb/°C. Obtainable from the ANP database.
Data are also provided in the ANP database to allow calculation of non-rated thrust as a function of a thrust setting parameter. This is defined by some manufacturers as engine pressure ratio EPR, and by others as low-pressure rotor speed, or fan speed, N1 . When that parameter is EPR, equation B-1 is replaced by
| Fn/δ = E + F · VC + GA · h + GB · h2 + H · T + K1 · EPR + K2 · EPR2 | (B-2) |
where K1 and K2 are coefficients, from the ANP database that relate corrected net thrust and engine pressure ratio in the vicinity of the engine pressure ratio of interest for the specified aeroplane Mach number.
When engine rotational speed N1 is the parameter used by the cockpit crew to set thrust, the generalised thrust equation becomes
where
is the rotational speed of the engine's low-pressure compressor (or fan) and turbine stages, %
= (T + 273)/288,15, the ratio of the absolute total temperature at the engine inlet to the absolute standard air temperature at mean sea level [ref. 1].
are constants derived from installed engine data encompassing the N1 speeds of interest.
Note that for a particular aeroplane E, F, GA, GB and H in equations B-2 and B-3 might have different values from those in equation B-1.
Not every term in the equation will always be significant. For example, for flat-rated engines operating in air temperatures below the break point (typically 30 °C), the temperature term may not be required. For engines not flat rated, ambient temperature must be considered when designating rated thrust. Above the engine flat rating temperature, a different set of engine thrust coefficients (E, F, GA, GB and H) high must be used to determine the thrust level available. Normal practice would then be to compute Fn /δ using both the low temperature and high temperature coefficients and to use the higher thrust level for temperatures below the flat rating temperature and use the lower calculated thrust level for temperature above the flat rating temperature.
Where only low temperature thrust coefficients are available, the following relationship may be used:
| (Fn/δ)high = F · VC + (E + H · TB )·(1 – 0,006 · T)/(1 – 0,006 · TB ) | (B-4) |
where
high-temperature corrected net thrust (lbf),
breakpoint temperature (in the absence of a definitive value assume a default value of 30 °C).
The ANP database provides values for the constants and coefficients in equations B-1 to B-4.
For propeller driven aeroplanes, corrected net thrust per engine should be read from graphs or calculated using the equation
| Fn/δ = (326 · η · Pp/VT )/δ | (B-5) |
where
is the propeller efficiency for a particular propeller installation and is a function of propeller rotational speed and aeroplane flight speed
is the true airspeed, kt
is net propulsive power for the given flight condition, e.g. max takeoff or max climb power, hp
Parameters in equation B-5 are provided in the ANP database for maximum takeoff thrust and maximum climb thrust settings.
True airspeed VT is estimated from the calibrated airspeed VC using the relationship
where σ is the ratio of the air density at the aeroplane to the mean sea-level value.
Guidance on operation with reduced takeoff thrust U.K.
Often, aircraft takeoff weights are below maximum allowable and/or the available runway field length exceeds the minimum required with the use of maximum takeoff thrust. In these cases, it is common practice to reduce engine thrust below maximum levels in order to prolong engine life and, sometimes, for noise abatement purposes. Engine thrust can only be reduced to levels that maintain a required margin of safety. The calculation procedure used by airline operators to determine the amount of thrust reduction is regulated accordingly: it is complex and takes into account numerous factors including takeoff weight, ambient air temperature, declared runway distances, runway elevation and runway obstacle clearance criteria. Therefore the amount of thrust reduction varies from flight to flight.
As they can have a profound effect upon departure noise contours, modellers should take reasonable account of reduced thrust operations and, to make best possible provision, to seek practical advice from operators.
If such advice is not available it is still advisable to make some allowance by alternative means. It is impractical to mirror the operators' calculations for noise modelling purposes; nor would they be appropriate alongside the conventional simplifications and approximations which are made for the purposes of calculating long term average noise levels. As a practicable alternative the following guidance is provided. It should be emphasised that considerable research is ongoing in this area and thus, this guidance is subject to change.
Analysis of FDR data has shown that the level of thrust reduction is strongly correlated with ratio of the actual takeoff weight to the Regulated Takeoff Weight (RTOW), down to a fixed lower limit(1); i.e.
| Fn/δ = (Fn/δ) max · W/WRTOW | (B-7) |
where (Fn /δ) max is the maximum rated thrust, W is the actual gross take-off weight and WRTOW is the Regulated Takeoff Weight.
The RTOW is the maximum takeoff weight that can be safely used, whilst satisfying takeoff field length, engine-out and obstacle requirements. It is a function of the available runway length, airfield elevation, temperature, headwind, and flap angle. This information can be obtained from operators and should be more readily available than data on actual levels of reduced thrust. Alternatively, it may be computed using data contained in aircraft flight manuals.
Reduced Climb Thrust U.K.
When employing reduced take-off thrust, operators often, but not always, reduce climb thrust from below maximum levels(2). This prevents situations occurring where, at the end of the initial climb at take-off thrust, power has to be increased rather than cut back. However, it is more difficult to establish a rationale for a common basis here. Some operators use fixed detents below maximum climb thrust, sometimes referred to as Climb 1 and Climb 2, typically reducing climb thrust by 10 and 20 percent respectively relative to maximum. It is recommended that whenever reduced takeoff thrust is used, climb thrust levels also be reduced by 10 percent.
Airworthiness authorities normally stipulate a lower thrust limit, often 25 percent below maximum.
To which thrust is reduced after the initial climb at take-off power.